/**
 * date   : 2026-09-19 14:14:02
 * author : Nyaan
 */

#define NDEBUG


#include <vector>

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <optional>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility

namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  constexpr P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  unsigned long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan


// bit operation

namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan


// inout

namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan


// debug


#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif


// macro

#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)


namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }






using namespace std;

namespace internal {
unsigned long long non_deterministic_seed() {
  unsigned long long m =
      chrono::duration_cast<chrono::nanoseconds>(
          chrono::high_resolution_clock::now().time_since_epoch())
          .count();
  m ^= 9845834732710364265uLL;
  m ^= m << 24, m ^= m >> 31, m ^= m << 35;
  return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }

// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(DETERMINISTIC_SEED)
  return deterministic_seed();
#elif defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
  return deterministic_seed();
#else
  return non_deterministic_seed();
#endif
}

}  // namespace internal


namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;

// [0, 2^64 - 1)
u64 rng() {
  static u64 _x = internal::seed();
  return _x ^= _x << 7, _x ^= _x >> 9;
}

// [l, r]
i64 rng(i64 l, i64 r) {
  assert(l <= r);
  return l + rng() % u64(r - l + 1);
}

// [l, r)
i64 randint(i64 l, i64 r) {
  assert(l < r);
  return l + rng() % u64(r - l);
}

// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
  assert(l <= r && n <= r - l);
  unordered_set<i64> s;
  for (i64 i = n; i; --i) {
    i64 m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<i64> ret;
  for (auto& x : s) ret.push_back(x);
  sort(begin(ret), end(ret));
  return ret;
}

// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
  assert(l < r);
  return l + rnd() * (r - l);
}

template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}

}  // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;



using namespace std;

struct Timer {
  chrono::high_resolution_clock::time_point st;

  Timer() { reset(); }
  void reset() { st = chrono::high_resolution_clock::now(); }

  long long elapsed() {
    auto ed = chrono::high_resolution_clock::now();
    return chrono::duration_cast<chrono::milliseconds>(ed - st).count();
  }
  long long operator()() { return elapsed(); }
};


//
using namespace Nyaan;

namespace miscalc {

#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define repi1(i, n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i, l, r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i, l, r, d)                              \
  for (int i = int(l), rrrrr = int(r), ddddd = int(d); \
       ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define eb emplace_back

template <class T = ll, class V>
inline T SZ(const V& x) {
  return x.size();
}

template <size_t MAX_M>
struct MatrixMod2 : vc<bitset<MAX_M>> {
  using M = MatrixMod2;
  using V = bitset<MAX_M>;
  using vc<bitset<MAX_M>>::vector;
  using vc<bitset<MAX_M>>::operator=;
  using vc<bitset<MAX_M>>::size;

  int m;
  MatrixMod2(int n, int m, int diag = 0, int non_diag = 0) : m(m) {
    assert(m <= (int)MAX_M);
    this->resize(n);
    repi(i, n) repi(j, m)(*this)[i][j] = i == j ? diag : non_diag;
  }
  template <class T>
  MatrixMod2(const vvc<T>& vec) {
    const int n = vec.size();
    m = n == 0 ? 0 : vec[0].size();
    assert(m <= (int)MAX_M);
    this->resize(n);
    repi(i, n) {
      assert(SZ(vec[i]) == m);
      repi(j, m) {
        assert(vec[i][j] == T(0) || vec[i][j] == T(1));
        (*this)[i][j] = vec[i][j];
      }
    }
  }
  MatrixMod2(const vc<string>& vec) {
    const int n = vec.size();
    m = n == 0 ? 0 : vec[0].size();
    assert(m <= (int)MAX_M);
    this->resize(n);
    repi(i, n) {
      assert(SZ(vec[i]) == m);
      repi(j, m) {
        assert(vec[i][j] == '0' || vec[i][j] == '1');
        (*this)[i][j] = vec[i][j] - '0';
      }
    }
  }
  template <class T = ll>
  vvc<T> to_vvi() const {
    const int n = size();
    vvc<T> res(n, vc<T>(m));
    repi(i, n) repi(j, m) res[i][j] = (*this)[i][j];
    return res;
  }
  vc<string> to_vstr() const {
    const int n = size();
    vc<string> res(n, string(m, '0'));
    repi(i, n) repi(j, m) res[i][j] += (*this)[i][j];
    return res;
  }

  M operator-() const { return *this; }

  // 加算・減算 O(nm/w)
  M& operator+=(const M& b) {
    const int n = size();
    repi(i, n)(*this)[i] ^= b[i];
    return *this;
  }
  M& operator-=(const M& b) { return *this += b; }
  M operator+(const M& b) const { return M(*this) += b; }
  M operator-(const M& b) const { return M(*this) -= b; }

  // 乗算 O(nmk/w)
  template <size_t MAX_K>
  MatrixMod2<MAX_K> operator*(const MatrixMod2<MAX_K>& b) const {
    const int n = size(), m_ = b.size(), k = b.m;
    assert(m == m_);
    MatrixMod2<MAX_K> res(n, k);
    repi(i, n) {
      auto row = (*this)[i];
      for (int j = row._Find_first(); j < m; j = row._Find_next(j))
        res[i] ^= b[j];
    }
    return res;
  }
  template <size_t MAX_K>
  MatrixMod2<MAX_K> operator*=(const MatrixMod2<MAX_K>& b) {
    return *this = *this * b;
  }

  // 正方行列
  // O(n^3 log k / w)
  template <class T>
  M pow(T k) const {
    const int n = size();
    assert(n == m);
    M res(1), tmp(*this);
    while (k > 0) {
      if (k & 1) res *= tmp;
      tmp *= tmp;
      k >>= 1;
    }
    return res;
  }

  // rref が true の場合、簡約行列にしたものを返す
  // rref が false の場合、階段行列にしたものを返す
  // O(nm min(n, m) / w)
  M row_reduction(bool rref = false) const {
    const int n = size();
    M a(*this);
    for (int i = 0, j = 0; i < n && j < m; j++) {
      repi(k, i, n) {
        if (a[k][j]) {
          swap(a[i], a[k]);
          break;
        }
      }
      if (a[i][j] == 0) continue;
      if (rref) repi(k, i) if (a[k][j]) a[k] ^= a[i];
      repi(k, i + 1, n) if (a[k][j]) a[k] ^= a[i];
      i++;
    }
    return a;
  }
  // O(nm min(n, m) / w)
  template <class I = ll>
  I rank() const {
    const int n = size();
    M a = row_reduction();
    I res = 0;
    repi(i, n) if (a[i] != 0) res++;
    return res;
  }
  // 正方行列、O(n^3/w)
  template <class I = ll>
  I det() const {
    const int n = size();
    assert(n == m);
    M a = row_reduction();
    I res = 1;
    repi(i, n) res &= a[i][i];
    return res;
  }
  // 正方行列、O(n^3/w)
  // (存在するか, 存在する場合逆行列)
  pair<bool, M> inv() const {
    const int n = size();
    assert(n == m);
    MatrixMod2<MAX_M * 2> a(n, 2 * n);
    repi(i, n) repi(j, n) a[i][j] = (*this)[i][j];
    repi(i, n) a[i][n + i] = 1;
    auto b = a.row_reduction(true);
    repi(i, n) if (b[i][i] == 0) return {false, {}};
    M res(n, n);
    repi(i, n) repi(j, n) res[i][j] = b[i][n + j];
    return {true, res};
  }

  // (解が存在するか, 解のひとつ, 基底)
  // O(nm min(n, m) / w + m^2
  template <size_t MAX_N>
  tuple<bool, V, vc<V>> solve(const bitset<MAX_N>& b) const {
    const int n = size();
    assert(n <= (int)MAX_N);
    MatrixMod2<MAX_M + 1> a(n, m + 1);
    repi(i, n) rep(j, m) a[i][j] = (*this)[i][j];
    repi(i, n) a[i][m] = b[i];
    a = a.row_reduction(true);
    int rk = 0;
    repi(i, n) if (a[i] != 0) rk++;

    V sol;
    vc<V> basis;
    vc<int> piv(m, -1);
    for (int i = 0, j = 0; i < rk; i++) {
      while (j < m && a[i][j] == 0) j++;
      if (j == m) return {false, {}, {}};
      sol[j] = a[i][m], piv[j] = i;
    }
    repi(j, m) {
      if (piv[j] != -1) continue;
      V ba;
      ba[j] = 1;
      repi(k, j) if (piv[k] != -1) ba[k] = a[piv[k]][j];
      basis.eb(ba);
    }
    return {true, sol, basis};
  }
};

}  // namespace miscalc

void q() {
  ini(N);
  V<string> S(N);
  in(S);

  vvi A(N, vi(N));
  rep(i, N) rep(j, N) A[i][j] = S[i][j] == '#' ? 1 : 0;

  set<tuple<int, int, int>> ans;

  auto flip_square = [&](int k, int r, int c) {
    V<pi> res;
    reg(i, -k, k + 1) {
      res.emplace_back(r + i, c + i);
      if (i != 0) res.emplace_back(r + i, c - i);
    }
    return res;
  };
  auto add = [&](int k, int r, int c) {
    each2(i, j, flip_square(k, r, c)) A[i][j] ^= 1;
    if (ans.count({k, r + 1, c + 1})) {
      ans.erase({k, r + 1, c + 1});
    } else {
      ans.insert({k, r + 1, c + 1});
    }
  };

  vp kouho;
  rep(i, N) rep(j, N) {
    if (i < 2 or j < 2 or i + 2 >= N or j + 2 >= N) kouho.emplace_back(i, j);
  }
  int C = sz(kouho);
  trc2(C);
  auto pos = [&](int i, int j) {
    auto k = lb(kouho, pl{i, j});
    if (k == sz(kouho) or kouho[k] != pl{i, j}) return -1;
    return k;
  };
  // 外周 2x2 で掃き出し
  constexpr int X = 12032;
  using bs = bitset<X>;
  V<bs> M(C);
  each(b, M) b.reset();
  V<tuple<int, int, int>> sousa;
  for (int k : {1, 2, 3}) {
    reg(r, k, N - k) reg(c, k, N - k) {
      bs b;
      b.reset();
      auto f = flip_square(k, r, c);
      int exist = 0;
      each2(i, j, f) exist |= pos(i, j) != -1;
      if (!exist) continue;
      each2(i, j, f) {
        int p = pos(i, j);
        if (p != -1) M[p].set(sz(sousa));
      }
      sousa.emplace_back(k, r, c);
      if (sz(sousa) >= X) exit(1);
    }
  }

  int D = sz(sousa);
  trc2(D);

  miscalc::MatrixMod2<X> MM(C, D);
  rep(i, C) rep(j, D) if (M[i][j]) MM[i].set(j);
  bitset<X> bb;
  bb.reset();
  rep(c, C) {
    auto [i, j] = kouho[c];
    if (A[i][j]) bb.set(c);
  }
  auto [flag, sol, basis] = MM.solve(bb);
  if (!flag) die(-1);

  rep(d, D) if (sol[d]) {
    auto [k, r, c] = sousa[d];
    add(k, r, c);
  }
  rep(i, N) rep(j, N) {
    if (A[i][j]) {
      assert(2 <= i and i + 2 < N);
      assert(2 <= j and j + 2 < N);
      add(1, i - 1, j - 1);
      add(1, i - 1, j + 1);
      add(1, i + 1, j - 1);
      add(1, i + 1, j + 1);
      add(2, i, j);
    }
  }

  out(sz(ans));
  for (auto& [k, r, c] : ans) out(k, r, c);
}

void test() {}

void Nyaan::solve() {
#ifdef NyaanLocal
  // test(); trc2("test OK");
#endif
  Timer timer;
  int t = 1;
  // in(t);
  while (t--) q();
  trc2(timer());
}